A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #7 #, its base has sides of length #5 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

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Answer 1 · 2018-06-21T11:55:43

#color(brown)(T S A = A_b + L S A = 21.65 + 74.3 = 95.95 " sq units"#

#h = 7, a = 5, theta = (2pi) / 3#

#"Area of base " = A_b = a^2 sin theta = 5^2 sin ((2pi)/3) = 21.65#

#"Slant height " = l = sqrt((a/2)^2 + h^2) = sqrt((5/2)^2 + 7^2) = 7.43#

#"Lateral Surface Area " = L S A = 4 * (1/2) * a * l = 2 * 5 * 7.43 = 74.3#

#color(brown)(T S A = A_b + L S A = 21.65 + 74.3 = 95.95 " sq units"#